Cheating Partner

I just have some questions to ask and I'm not looking for judgement. But I need help. A bit of a long one sorry.

I've been with my boyfriend only a short period of time, about 2-3 months. We had a party with a few friends the other night and we all got really drunk.

My boyfriend is 25 and slept with an 18 year old in the same house as I was asleep in.

I'm really hurt by this of course, but I'm willing to work through this if he proves to me he cares enough to work past this.

He explained to me he'd done it before in a past relationship too which concerns me, but I really like him and I want to see him become a better person.

It's not my place to try ans change him. He says he doesn't know why he did it, and says he still likes me. I want it to work because I was happy before this.

Am I silly for wanting to try and make this work?

EDIT: I'm giving him a couple of days to decide whether or not he wants to work on us or be single.